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Problem 2: Two very long, slender rods of the same diameter and length are given. One rod (Rod 1) is made of aluminum and has a thermal conductivity k1 = 200 W/m-K, but the thermal conductivity of Rod 2, k2 is not known. To determine the ther- mal conductivity of Rod 2, both rods at one end are thermally attached to a metal surface which is maintained at a constant temperature Tb. Both rods are losing heat by convection, with a convection heat transfer coefficient h into the ambient air at Too. The surface temperature of each rod is measured at various distances from the hot base surface. The measurements reveal that the temperature of the aluminum rod (Rod 1) at X1 = 40 cm from the base is the same as that of the rod of unknown thermal conductivity (Rod 2) at X2 = 20 cm from the base. Determine the thermal conductivity k2 of the second rod (W/m-K). k1 = 200 W/m-K Rod 1 To X1 1=40cm T1(x) h, To 8 Rod 2 X2 = 20 cm T2(x) X

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